# Victoria University Antarctic Research Expedition Science and Logistics Reports 1980-81: VUWAE 25

# G. Ray Tracing Analysis

### G. Ray Tracing Analysis

The analysis used here is suitable for this situation where the refracting interface being mapped is sharply curved, so ray paths don't travel along the interface and leave at the critical angle, but instead cut through the bulk of the material.

You need to know the structure above the interface and the depth of the interface either under the spread or the shot point, as well as the velocity below the interface. In the present case the interface was the basement surface, and was fairly flat near shot point II (SP II) and its depth Z_{A} was obtained from the time intercept as SP II.

#### METHOD

Using the plane-layer structure already determined for the overlying sediments, and the apparent velocity of the spread, the ray path can be calculated back to the point B on the bottom plane refractor, and the co-ordinates of B, the time to get from B to G (T_{BG}) and the angle θ_{n-1} at which the ray arrived worked out.

Also for the point A co-ordinates and time T_{SA} can be calculated from the known structure at A, assuming critical refraction. For the case where q is large compared to the depth the point A is fairly constant for all spreads since the angle of the ray path along q changes very fast with a change in the incoming ray angle near the critical angle.

Having calculated the co-ords (X, Z, T) of points A, B, and the angle θ_{n-1} you can set up simultaneous equations and solve a quadratic for Y and hence the position of the basement.

(5) is a quadratic in Y and is readily solved from which the sensible value of Y is taken and the co-ordinates of the basement refraction point R can be worked out.

page 54This method was used for arrivals on spreads 3-9 from shot point II and on spreads 1-4 from shot point III to obtain the structure between shot points II and III. This structure was used, together with arrivals on spreads 1, 3, 4 and 4 from shot point IV, to locate the basement refraction point on the descending ray from shot point IV, assuming that the ray had the same angle in the water as the reverse rays from shot point II to spread 9, which was only 660m from shot point IV. The ray path from the shot point was traced down to the bottom plane layer refractor and the equation (5) solved.

The solutions gave the group of X's marked down at approximately 1500m depth on the profile diagram. Using the mean position of these points as the true position of the basement refraction point on the descending ray path from SP IV and using the single 2600 sedimentary layer in order to be consistent with the 3398 and 3146 arrivals, the equations were solved for the 22400 arrival and this gave the X marked at 1026m depth.